Spin-orbit Coupling and Multiple Phases in Spin-triplet Superconductor Sr${}_2$RuO${}_4$

Abstract

We study the spin-orbit coupling in spin-triplet Cooper pairs and clarify multiple superconducting (SC) phases in Sr${}_2$RuO${}_4$. Based on the analysis of the three-orbital Hubbard model with atomic LS coupling, we show some selection rules of the spin-orbit coupling in Cooper pairs. The spin-orbit coupling is small when the two-dimensional $\gamma$-band is the main cause of the superconductivity, although the LS coupling is much larger than the SC gap. Considering this case, we investigate multiple SC transitions in the magnetic fields for both H // [001] and H // [100] using the Ginzburg-Landau theory and the quasi-classical theory. Rich phase diagrams are obtained because the spin degree of freedom in Cooper pairs is not quenched by the spin-orbit coupling. Experimental indications for the multiple phases in Sr${}_2$RuO${}_4$ are discussed.

arXiv commentPublished in "Special Topics: Advances in Physics of Strongly Correlated Electron Systems" of J. Phys. Soc. Jpn. based on an invited talk at SCES2013

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• Specific-heat evidence of the first-order superconducting transition in Sr2RuO4
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• Spin-orbit coupling and spin-triplet pairing symmetry in $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$
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• Time-reversal symmetry breaking superconductivity in hole-doped monolayer MoS${}_2$
• Identification of Spin-Triplet Superconductivity through a Helical-Chiral Phase Transition in Sr${}_2$RuO${}_4$ Thin-Films
• Spin-orbit coupling and odd-parity superconductivity in the quasi-one-dimensional compound Li${}_{0.9}$Mo${}_6$O${}_{17}$
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